stivali ugg Convergence of non-standard filter cha

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Convergence of filter characteristics and applications of non-standard

Co A. Theorem 4 net {Mao, D,>} converge to the point,[link widoczny dla zalogowanych], if and only if the export filter converges to points. Proof (necessity) network convergence at the point z, the net convergence of the non-standard features we know, for any D in the infinite element, hair ∈ (): n {. G: G ∈}, that is, for any G ∈ 0,[link widoczny dla zalogowanych], ∈ G.Is the export filter, so G ∈. So n {. F: F ∈} c (). Convergence of the non-standard features of filter, filter converges to points. (Adequacy) is the net export filter, defined by the export filter. = {F: finally F}. By Lemma 3, for any F ∈, for any infinite D, Tai Yuen v, ∈ F, so ∈ n {F: F ∈. }. They converge to the point of convergence of the non-standard by the filter characteristics of known, n {F: F ∈} I = (), and thus ∈ (), non-standard features of the network convergence, network convergence at the point. Theorem 5 filter converges to point, if and only if every point of convergence of derived net. Proof (necessity) is derived from the filter network, so} = (V ∈ D) (V ∈ D) (> a F1cF),[link widoczny dla zalogowanych], the conversion mechanism. } = (V ∈ D) (V ∈ D) (> A FF). So take as. D in any infinite Tai Yuen, to D, any element,[link widoczny dla zalogowanych], obviously > , then F1cF2, so Fc {'F: F ∈}. And () ∈ F,, so () ∈ n {F: F ∈}. The filter in the convergent point of convergence of the filter of non-standard features, n {F: F ∈} c (). Then () ∈ (z), non-standard features of the network convergence, network convergence at the point. 1 filter runoff and other non-standard features of convergence and its applications (full of) anti-set filter does not converge at the point, then there exists G ∈, so G ∈. Then for any D, , FG. So take ∈ F-G, a () G, by the transfer principle, for arbitrary D, , a () G, thus ( ) (). Non-standard features of the network convergence, network does not converge to the point, which conflicts with the question set, so the filter converges to points.
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